A Model for an Applied Mathematics Internship Program

The Department of Mathematics at the City University of New York’s New York City College of Technology (City Tech) began offering an applied mathematics major in 2004. The program has since found much success, with enrollment growing from only seven majors at its onset to approximately 100 in 2016. Our internship requirement is a key part of this success.

City Tech’s students come from more than 100 different countries. Many are first-generation college-goers, and often need employment immediately after graduation. While some of the internships are paid, it is more essential that the work experience helps students reach their career objectives. Six of the 12 interns in our spring 2016 cohort remained at the institution where they completed their internships, and 10 of the 12 intern supervisors indicated that their agency, or a similar organization, would likely hire the intern. This suggests that even more interns could have found employment at their internship sites, but decided to go on to graduate school or look for another position.

In the following sections, we discuss our management and assessment of the internship program. We also provide some case studies, which highlight the utility of mathematics in atypical settings.

Finding Internships

Figure 1. Breakdown of internship types for students in the Department of Mathematics at City Tech. The data is based on 139 internships over the past 12 years. Figure credit: Nadia Benakli and Jonathan Natov.

Students in City Tech’s applied math program are required to complete two internships. Students submit statements of career objectives at the beginning of the process, which help determine appropriate internship opportunities. They are responsible for finding appropriate positions, with some help from faculty, and can also access City Tech’s Professional Development Center for possible opportunities and on-campus recruiting events.

While some students complete their internships in “conventional” host organizations, such as financial institutions, educational foundations, or research labs, many internship opportunities come as a surprise, as evidenced in the following case studies. Figure 1 presents a breakdown of students’ internship types, based on 139 internships over the last 12 years.

Case Studies

Many of our interns have discovered interesting opportunities for mathematics and consequently broadened our perspective of what an internship might look like. Their successes reinforce our belief that mathematics has a role to play in almost every industry.

Transportation. One applied mathematics major obtained a paid job working on signal repairs for the New York City Metropolitan Transportation Authority (MTA). Many of our students work part time or full time while pursuing their degrees, and City Tech has an established relationship with the MTA.

The opportunity arose during the performance of a mandated test to determine the condition of batteries, which identify the position of trains in the event of a power outage. By collecting data and using a simple regression analysis, the student estimated the longevity of battery life. This work became the basis for his first internship.

Given the vast amounts of data that have been collected but not yet analyzed, the intern believes that his data analysis skills will yield many opportunities to improve the system.

Transportation: Railroad. Another transportation-related example involves a student who worked at a leading railroad company to support his family. Though his job focused on routine tasks, he astutely noticed that a certain switch often broke down during system failures, causing significant problems and passenger delays. He downloaded a student version of a statistical application, taught himself the necessary commands, collected data, and presented the analysis to his supervisor.

By replacing an inexpensive switch, the railroad significantly reduced the system failures. In response, the railroad management hired the student as a systems analyst and supported him while he completed a graduate program.

Call Center. Yet another student wished to ultimately find employment with a financial institution. Her internship experience began while working for a city agency, answering calls and directing callers to the appropriate department. While this did not qualify as an internship, she took the initiative to keep track of the approximate number of calls the center received. She then created a statistical model to determine a confidence interval that estimated the likely number of callers within an hour. Her work showcased inferential statistics and impressed her supervisor.

This intern then moved on to a position as a budget analyst for a car rental agency, which led to a job as an analyst at a prestigious financial institution.

Pharmacy. When one of our majors began working for a pharmaceutical company, his job essentially involved running errands. However, he looked for opportunities to use his skills. He noticed that the company tended to purchase relatively small amounts of chemicals, and wondered if purchasing in bulk could save money. But price fluctuations cause uncertainty, and the company was unfamiliar with the cost of larger quantities of chemicals.

The student produced a price estimate using a regression analysis, which closely matched the actual price the company would have to pay. His applied mathematics skills promoted him from running errands to running budget analyses.

Teachers’ Union. While a teachers’ union might not seem like an obvious place for an applied math student, one of our interns found unexpected success. The union in question is part of an umbrella organization to which it must pay dues. At the start of a new billing cycle, the union can choose from a few different payment formulas.

Formulas are based on the number of full- and part-time faculty members, higher education officers, and their corresponding ranks. Computing the cost involved a large data set (in the tens of thousands); unpredictable fluctuation of the numbers was an added complication. Our intern helped create a pricing model to accurately determine the cost of each payment option. In so doing, he helped the union save hundreds of thousands of dollars each year.

Data Science. A student found a position at a company that analyzes television viewership data. The company developed both a proprietary application to quantify qualitative data and a benchmarking application to test the proprietary application’s success.

After graduation, the student landed a full-time job with the company, which subsequently took on two more interns. As a result of our students’ many successes, companies are beginning to approach us for interns. With time, we expect growing demand for our applied math majors.

Assessing the Internships

We assess internships based on a supervisor’s evaluation, a log of the intern’s activities, a final written report, an oral presentation, the student’s professionalism, and the significance and relevance of their work to the overall goals of the organization.

Interns are expected to behave as professionals, which involves using terminology appropriate for industry, writing professional documents, respecting deadlines, keeping scheduled appointments, and conducting themselves with integrity and respect.

Written reports submitted by interns include information on the host organization; an overview of the intern’s responsibilities, duties, and overall experience; and insights as to how the intern’s contributions benefited the company. Keeping a work log helps interns evaluate their work and monitor their progress while recording their weekly tasks and new skills.

Towards the end of the semester, interns present their work. They focus on essentials, respond to audience questions, and are expected to use their limited time wisely.

Finally, we also consider the significance of internship work for overall evaluation. By the end of their second internship, students should be prepared to meet their career objectives.

Ensuring a Strong Curriculum

The internship experience is the heart of City Tech’s applied mathematics program, and serves three essential functions. First, it helps graduates find meaningful employment. A successful internship provides strong evidence of future success in industry, which assists our graduates as they compete against candidates from more prestigious institutions.

Secondly, it ensures that our curriculum meets industry’s current demands and incorporates current applications of mathematics that are of interest and relevant to industry.

Ultimately, internships provide a way to assess the strengths and weaknesses of our program. For example, supervisors have generally been impressed with our interns’ mathematical skills. However, ratings of their communication skills were typically lower. In response, we modified our math modeling courses to include more written reports and oral presentations. This change has correlated with improved ratings.

We strongly recommend that applied math programs require internships, in order to foster strong mathematical training and keep students competitive. Our experience has shown that internships are manageable and crucial for a career-oriented program.

Nadia Benakli is an associate professor of mathematics at New York City College of Technology of the City University of New York (CUNY). She is the coordinator of the applied mathematics internship program. Jonathan Natov is a professor of mathematics at NYC College of Technology. He coordinated the applied mathematics program from 2004 to 2014.

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